Should You Grab The Abandoned Onions?

You are planning a nice dinner and are shopping for the necessary groceries. After having already passed the green onions you are reminded that you actually need green onions upon discovering exactly that vegetable, in a bunch, bagged, and apparently abandoned by another shopper. Do you grab the bag before you or turn around and go out of your way to select your own bunch?

This bag was selected already, and from a weakly larger supply. It is therefore likely to be better than the best you will find there now.

On the other hand, it was abandoned. You have to ask yourself why.

You would worry if the typical shopper’s strategy is to select a bag at random and then only carefully inspect it later. Because then it was abandoned because of some defect.

But this a red herring. Whatever she could see wrong with the onions you can see too. The only asymmetry of information between you and your pre-shopper is about the unchosen onions. The selection effect works unambiguoulsy in favor of the scallions-in-hand.

You can gain information based on where the onions were abandoned.

First of all the fact that they were abandoned somewhere other than the main pile of onions reveals that she was not rejecting these in favor of other onions. If so, since she was going back to the onion pile she would have brought these with her. Instead she probably realized that she didn’t need the onions after all. So again, no negative signal.

If these bunched green onions were abandoned in front of the loose green onions or the leeks or ramps, then this is an even better signal. She thought these were the best among the green onions but later discovered an even better ingredient. A sign she has discerning tastes.

It is true though that compared to a randomly selected new bunch, these have been touched by on average one additional pair of human hands.

And also she might be trying to poison you.

But if she was trying to poison someone, is it her optimal strategy to put the poisoned onions into a bag and abandon them in a neighboring aisle?

In equilibrium all bunches are equally likely to be poisoned and the bagging and abandoning ploy amounts to nothing more than cheap talk.

But, she might not be trying to poison just any old person. She might really be targeting you, the guy who wants the best bunch of onions in the store.

Therefore these onions are either logically the best onions in the store and therefore poisoned, or they are worse than some onions back in the big pile but then those are poisoned.